Script not working properly with FilteringEnabled?

Ok, after a lot of playing around i've come up with a workable solution. It seems to be the case that CFraming your character locally and even moving it locally with a BodyPosition replicate to the server just fine even with filtering enabled on. This seems weird to me and an easy vector for exploit, but it does make creating the functionality you want fairly easy. It isn't exactly like the code you had posted, as you can't look up or down to move up/down - you have to use space/left ctrl, but adding that functionality introduced other problems so I thought it was better this way. The character is also playing the falling animation when no clip is active, but you can always add to the code below to play a custom animation if it is important to you.

This should be in a local script in StarterPlayerScripts. It handles input, messaging the server to turn on/off collision, the BodyPosition that controls hovering, and I also rotate the character in a renderstep that runs after camera update to get smooth rotations. I have commented the two variables you can change here to control noclip speed.

local UserInputService = game:GetService("UserInputService")
local player = game.Players.LocalPlayer
local MasterControl = require(player:WaitForChild("PlayerScripts"):WaitForChild("ControlScript"):WaitForChild("MasterControl"))
local noClipEvent = game.ReplicatedStorage:WaitForChild("NoClipEvent")
local isNoClipActive = false
local isSpaceHeld = false
local isCtrlHeld = false
local hoverHeight
local lastUpdate

local bodyPosition = Instance.new("BodyPosition")
bodyPosition.Name = "NoClipBodyPosition"
bodyPosition.MaxForce = Vector3.new(500000000, 500000000, 500000000)
bodyPosition.D = 400

-- These two variables will change the noclip horizontal and vertical speeds respectively
local noClipSpeed = 40
local hoverIncrementSpeed = 1

UserInputService.InputBegan:connect(function(input, event)
    if not event then
		if input.KeyCode == Enum.KeyCode.ButtonB or input.KeyCode == Enum.KeyCode.V then
			if player.Character and player.Character.Parent then
				lastUpdate = tick()
		        isNoClipActive = not isNoClipActive
		        noClipEvent:FireServer(isNoClipActive)
				MasterControl:SetNoClip(isNoClipActive, noClipSpeed)
		
				if isNoClipActive then
					local root = player.Character:FindFirstChild("HumanoidRootPart")
					if root then
						bodyPosition.Parent = player.Character.HumanoidRootPart
						bodyPosition.Position = root.Position
						hoverHeight = root.Position.Y
					end
				else
					bodyPosition.Parent = nil
				end
			end
		end
		if input.KeyCode == Enum.KeyCode.Space then
			isSpaceHeld = true
		end
		if input.KeyCode == Enum.KeyCode.LeftControl then
			isCtrlHeld = true
		end
    end
end)

UserInputService.InputEnded:connect(function(input, event)
	if not event then
		if input.KeyCode == Enum.KeyCode.Space then
			isSpaceHeld = false
		end
		if input.KeyCode == Enum.KeyCode.LeftControl then
			isCtrlHeld = false
		end
	end
end)

game:GetService("RunService"):BindToRenderStep("updateLoop", Enum.RenderPriority.Camera.Value + 1, function()
	if isNoClipActive and player.Character and player.Character.Parent then
		local root = player.Character:FindFirstChild("HumanoidRootPart")
		if root then
			local cam = workspace.CurrentCamera
			local camForward = cam.CFrame.lookVector
			camForward = Vector3.new(camForward.X, 0, camForward.Z).Unit
			root.CFrame = CFrame.new(root.CFrame.p, root.CFrame.p + camForward)
			
			if isSpaceHeld then
				hoverHeight = hoverHeight + hoverIncrementSpeed
			end
			if isCtrlHeld then
				hoverHeight = hoverHeight - hoverIncrementSpeed
			end
			if bodyPosition.Parent then
				bodyPosition.Position = Vector3.new(root.CFrame.p.X, hoverHeight, root.CFrame.p.Z)
			end
		end
	end
end)

This is a server script that should be in ServerScriptService. It's job is to toggle player collision on/off when it receives a message from the local script.

local PhysicsService = game:GetService("PhysicsService")
local Players = game:GetService("Players")

local noClipEvent = Instance.new("RemoteEvent")
noClipEvent.Name = "NoClipEvent"
noClipEvent.Parent = game.ReplicatedStorage

local noClipPlayers = "Players"
PhysicsService:CreateCollisionGroup(noClipPlayers)
PhysicsService:CollisionGroupSetCollidable("Default", noClipPlayers, false)

local function setCollisionGroupRecursive(object, groupName)
    if object:IsA("BasePart") then
        PhysicsService:SetPartCollisionGroup(object, groupName)
    end
    for _, child in ipairs(object:GetChildren()) do
        setCollisionGroupRecursive(child, groupName)
    end
end

noClipEvent.OnServerEvent:connect(function(player, isNoClipActive)
    local character = player.Character
    if character then
        if isNoClipActive then
            setCollisionGroupRecursive(character, noClipPlayers)
        else
            setCollisionGroupRecursive(character, "Default")
        end
    end
end)

Finally, we have the code that updates player movement, which I have put in a modified ControlScript. This same code can be run within the local script and still work, but having it in the control script speeds things up a lot. You will see i'm also rotating the character here before moving it. You can get away with only having the character rotation updated here, and not also in the local script, but as this is bound to the input render priority, only having it updated here gives you jittery rotations. To set this up, you will want to press play in studio, and in the explorer navigate to Players -> [your player name] -> PlayerScripts and copy the ControlScript you find in there (Ctrl+C). Then press stop to exit the game, and paste the ControlScript into StarterPlayer -> StarterPlayerScripts. Then expand the ControlScript in the explorer and you will find the MasterControl module. Open MasterControl up for editing.

On lines 82 to 99 is the code for the updateMovement function. You need to replace these 18 lines with the following

local getHumanoid = MasterControl.GetHumanoid
local moveFunc = LocalPlayer.Move
local shouldUpdate = false
local lastUpdate
local updateMovement = function()
	
	if not areControlsEnabled then return end
	
	local humanoid = getHumanoid()
	if not humanoid then return end
	
	if isJumpEnabled and isJumping and not humanoid.PlatformStand then
		local state = humanoid:GetState()
		if state ~= STATE_JUMPING and state ~= STATE_FREEFALL and state ~= STATE_LANDED then
			humanoid.Jump = isJumping
		end
	end
	
	if allowNoClip then
		if shouldUpdate then
			shouldUpdate = false
			moveFunc(LocalPlayer, Vector3.new(), true)
			lastUpdate = tick()
		end
		
		local root = LocalCharacter:FindFirstChild("HumanoidRootPart")
		if root then
			local cam = workspace.CurrentCamera
			local camForward = cam.CFrame.lookVector
			camForward = Vector3.new(camForward.X, 0, camForward.Z).Unit
			local currentTime = tick()
			local delta = currentTime - lastUpdate
			root.CFrame = CFrame.new(root.CFrame.p, root.CFrame.p + camForward) * CFrame.new(moveValue * delta * noClipSpeed)
			lastUpdate = currentTime
		end
	else
		moveFunc(LocalPlayer, moveValue, true)
		shouldUpdate = true
	end
end

Above what you just pasted, you want to insert this code

local allowNoClip = false
local noClipSpeed = 40
function MasterControl:SetNoClip(isNoClipActive, speed)
	allowNoClip = isNoClipActive
	noClipSpeed = speed
end

So the area you just modified should now look like this

if LocalCharacter then
	characterAdded(LocalCharacter)
end
LocalPlayer.CharacterAdded:connect(characterAdded)

-- The above was already there. Your code starts below
local allowNoClip = false
local noClipSpeed = 40
function MasterControl:SetNoClip(isNoClipActive, speed)
	allowNoClip = isNoClipActive
	noClipSpeed = speed
end

local getHumanoid = MasterControl.GetHumanoid
local moveFunc = LocalPlayer.Move
local shouldUpdate = false
local lastUpdate
local updateMovement = function()
	
	if not areControlsEnabled then return end
	
	local humanoid = getHumanoid()
	if not humanoid then return end
	
	if isJumpEnabled and isJumping and not humanoid.PlatformStand then
		local state = humanoid:GetState()
		if state ~= STATE_JUMPING and state ~= STATE_FREEFALL and state ~= STATE_LANDED then
			humanoid.Jump = isJumping
		end
	end
	
	if allowNoClip then
		if shouldUpdate then
			shouldUpdate = false
			moveFunc(LocalPlayer, Vector3.new(), true)
			lastUpdate = tick()
		end
		
		local root = LocalCharacter:FindFirstChild("HumanoidRootPart")
		if root then
			local cam = workspace.CurrentCamera
			local camForward = cam.CFrame.lookVector
			camForward = Vector3.new(camForward.X, 0, camForward.Z).Unit
			local currentTime = tick()
			local delta = currentTime - lastUpdate
			root.CFrame = CFrame.new(root.CFrame.p, root.CFrame.p + camForward) * CFrame.new(moveValue * delta * noClipSpeed)
			lastUpdate = currentTime
		end
	else
		moveFunc(LocalPlayer, moveValue, true)
		shouldUpdate = true
	end
end
-- Your edits end here

--[[ Public API ]]--

And that's it. I apologize for the long post, but I wanted to be as clear as possible with everything. If you have any questions feel free to ask.